Principle Of Excluded Middle Quotes

It may be said very abstractly that in personality all persons are equal. But this is an empty tautological proposition, in logic identified with the law of mere identity or A = A. This is so because a person abstractly considered is not as yet separate from others, and has no distinguishing attribute. Equality is the abstract identity set up by the mere understanding. Upon this principle, mere impoverished reflecting thought, or, in other words, spirit in its middle ranges, is apt to fall, when before it there arises the relation of identity to difference. This equalit would be only the identity of abstract persons as such, and would exclude all reference to posession, which is the basis of inequality. Sometimes the demand is made for equality in the division of the soil of the earth, and even other kinds of wealth. The theory of a pious, friendly brotherhood of men who are to possess all goods in common, and to banish the principle of private ownership, easily presents itself to one who fails to understand the nature of freedom of spirit and nature of right, through mistaking their definite phases. Claims of a demand for equality in divisions of wealth are superficial, because the differences of wealth are due not only to the accidents of external nature but also to the infinite variety and difference of mental ability and character.

It seems to me that the doctrine of the laws of thought could be simplified if we were to set up only two, the law of excluded middle and that of sufficient reason. The former thus: "Every predicate can be either confirmed or denied of every subject." Here it is already contained in the "either, or" that both cannot occur simultaneously, and consequently just what is expressed by the laws of identity and contradiction. Thus these would be added as corollaries of that principle which really says that every two concept-spheres must be thought either as united or as separated, but never as both at once; and therefore, even although words are joined together which express the latter, these words assert a process of thought which cannot be carried out. The consciousness of this infeasibility is the feeling of contradiction. The second law of thought, the principle of sufficient reason, would affirm that the above attributing or refuting must be determined by something different from the judgment itself, which may be a (pure or empirical) perception, or merely another judgment. This other and different thing is then called the ground or reason of the judgment. So far as a judgment satisfies the first law of thought, it is thinkable; so far as it satisfies the second, it is true, or at least in the case in which the ground of a judgment is only another judgment it is logically or formally true.

If the principle of identity is at best only an incomplete truth, the principles of contradiction and of the excluded middle are complete untruths. Far from making a thought nonsense, contradiction is the very thing which unfolds and develops the thought, and hence, too, the object which it expresses. It is precisely opposition, or antithesis, which sets things in motion, which is the mainspring of evolution, which calls forth and develops the latent forces and powers of being.

the more profound the statement, the more reversible; the deep truths are sedimented in syntax, the terms can be reversed, just as there is no principle of noncontradiction, no law of excluded middle, governing the unconscious. Then, briefly serious, Klaus would touch my shoulder: A quote like that can save your life.

Now if we are to accept the common idea of continuity . . . we must either say that a continuous line contains no points or . . . that the principle of excluded middle does not hold of these points. The principle of excluded middle applies only to an individual . . . but places being mere possibilities without actual existence are not individuals.

On the basis of the testability just mentioned, there hold, for properties conceived within a specific finite main system, the "principle of excluded middle", that is, the principle that for every system every property is either correct [richtig] or impossible, and in particular the principle of the reciprocity of the complementary species, that is, the principle that for every system the correctness of a property follows from the impossibility of the impossibility of this property.

However, notwithstanding this rejection of classical logic as an instrument to discover mathematical truths, intuitionist mathematics has its general introspective theory of mathematical assertions, a theory which with some right may be called intuitionistic mathematical logic, and to which belongs a theory of the principle of the excluded middle. In intuitionism this principle is also called the principle of judgeability.

In social crisis and political revolution, when a government breaks down, power falls into the hands of the working masses; and for the propertied class, for capitalism arises the problem how to wrest it out of their hands. So it was in the past, so it may happen in the future. Democracy is the means, the appropriate instrument of persuasion. The arguments of formal and legal equality have to induce the workers to give up their power and to let their organization be inserted as a subordinate part into the State structure. Against this the workers have to carry in them a strong conviction that council organization is a higher and more perfect form of equality. It realizes social equality; it is the form of equality adapted to a society consciously dominating production and life. It might be asked whether the term democracy fits here, because the ending—"-cracy"—indicates domination by force, which here is lacking. Though the individuals have to conform to the whole there is no government above the people; people itself is government. Council organization is the very means by which working mankind, without need of a ruling government, organizes its vital activities. Adhering, then, to the emotional value attached of old to the word democracy we may say that council organization represents the higher form of democracy, the true democracy of labor. Political democracy, middle-class democracy, at its best can be no more than a formal democracy; it gives the same legal rights to everybody, but does not care whether this implies security of life; because economic life, because production is not concerned. The worker has his equal right to sell his labor power; but he is not certain that he will be able to sell it. Council democracy, on the contrary, is actual democracy since it secures life to all collaborating producers, free and equal masters of the sources of their life. The equal right in deciding needs not to be secured by any formal regulating paragraph; it is realized in that the work, in every part, is regulated by those who do the work. That parasites taking no part in production automatically exclude themselves from taking part in the decisions, cannot be considered as a lack in democracy; not their person but their function excludes them. It is often said that in the modern world the point of dispute is between democracy and dictatorship; and that the working class has to throw in its full weight for democracy. The real meaning of this statement of contrast is that capitalist opinion is divided whether capitalism better maintains its sway with soft deceitful democracy, or with hard dictatorial constraint. It is the old problem of whether rebellious slaves are kept down better by kindness or by terror. The slaves, if asked, of course prefer kind treatment to terror; but if they let themselves be fooled so as to mistake soft slavery for freedom, it is pernicious to the cause of their freedom. For the working class in the present time the real issue is between council organization, the true democracy of labor, and the apparent, deceitful middle-class democracy of formal rights. In proclaiming council democracy the workers transfer the fight from political form to economic contents. Or rather—since politics is only form and means for economy—for the sounding political slogan they substitute the revolutionizing political deed, the seizure of the means of production. The slogan of political democracy serves to detract the attention of the workers from their true goal. It must be the concern of the workers, by putting up the principle of council organization, of actual democracy of labor, to give true expression to the great issue now moving society.

New Deal legislation undoubtedly saved thousands of lives and prevented destitution for millions. New labor laws led to a flourishing of unions and built a strong white middle class. The Social Security Act of 1935 established the principle of cash payments in cases of unemployment, old age, or loss of a family breadwinner, and it did so as a matter of right, not on the basis of individual moral character. But the New Deal also created racial, gender, and class divisions that continue to produce inequities in our society today. Roosevelt’s administration capitulated to white supremacy in ways that still bear bitter fruit. The Civilian Conservation Corps capped Black participation in federally supported work relief at 10 percent of available jobs, though African Americans experienced 80 percent unemployment in northern cities. The National Housing Act of 1934 redoubled the burden on Black neighborhoods by promoting residential segregation and encouraging mortgage redlining. The Wagner Act granted workers the right to organize, but allowed segregated trade unions. Most importantly, in response to threats that southern states would not support the Social Security Act, both agricultural and domestic workers were explicitly excluded from its employment protections. The “southern compromise” left the great majority of African American workers—and a not-insignificant number of poor white tenant farmers, sharecroppers, and domestics—with no minimum wage, unemployment protection, old-age insurance, or right to collective bargaining.

I refer to a fundamental difference in the religious attitude between the East (China and India) and the West; this difference can be expressed in terms of logical concepts. Since Aristotle, the Western world has followed the logical principles of Aristotelian philosophy. This logic is based on the law of identity which states that A is A, the law of contradiction (A is not non-A) and the law of the excluded middle (A cannot be A and non-A, neither A nor non-A). Aristotle explains his position very clearly in the following sentence: 'It is impossible for the same thing at the same time to belong and not to belong to the same thing and in the same respect; and whatever other distinctions we might add to meet dialectical objections, let them be added. This, then, is the most certain of all principles...' This axiom of Aristotelian logic has so deeply imbued our habits of thought that it is felt to be 'natural' and self-evident, while on the other hand the statement that X is A and not A seems to be nonsensical. (Of course, the statement refers to the subject X at a given time, not to X now and X later, or one aspect of X as against another aspect.) In opposition to Aristotelian logic is what one might call paradoxical logic, which assumes that A and non-A do not exclude each other as predicates of X. Paradoxical logic was predominant in Chinese and Indian thinking, in the philosophy of Heraclitus, and then again, under the name of dialectics, it became the philosophy of Hegel, and of Marx. The general principle of paradoxical logic has been clearly described by Lao-tse. 'Words that are strictly true seem to be paradoxical.' And by Chuang-tzu: 'That which is one is one. That which. is not-one, is also one.' These formulations of paradoxical logic are positive: it is and it is not. Another formulation is negative: it is neither this nor that. The former expression of thought we find in Taoistic thought, in Heraclitus and again in Hegelian dialectics; the latter formulation is frequent in Indian philosophy. Although it would transcend the scope of this book to give a more detailed description of the difference between Aristotelian and paradoxical logic, I shall mention a few illustrations in order to make the principle more understandable. Paradoxical logic in Western thought has its earliest philosophical expression in Heraclitus philosophy. He assumes the conflict between opposites is the basis of all existence. 'They do not understand', he says, 'that the all-One, conflicting in itself, is identical with itself: conflicting harmony as in the bow and in the lyre.' Or still more clearly: 'We go into the same river, and yet not in the same; it is we and it is not we.' Or 'One and the same manifests itself in things as living and dead, waking and sleeping, young and old.